The vertical asymptote of a tangent for f(x) = 1/tan(pi*x)

[tttete7]

There is a multiple choice question in our book and I have been trying to find out why the answer is D for the past hour can someone please help me

Question: which of the values of x can't be the vertical asymptote of the function : f(x)= 1/tanpix

a) x= -5
b) x= 0
C)x= 1
d) x= 1/2

 

[Harry_the_cat]

Consider what happens when you substitute those 4 different values of x into that function.

Note: I'm assuming 1/tanpix means \(\displaystyle \frac{1}{\tan(\pi x)}\).

 

[skeeter]

note …

[imath]\dfrac{1}{\tan(\pi x)} = \dfrac{\cos(\pi x)}{\sin(\pi x)}[/imath]